Mrs. Smith's drama class is taking a field trip to the theater to watch a play. She needs to calculate the distance in order to reserve the bus for the day. What is the distance from the school to the theater? Show your work and leave your
answer in simplest radical form if necessary.

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula.

The distance formula is:

So, we want to find the distance between the school and the theater.

We can see that the school is at the point (8,7).

And the theater is at the point (2,3).

So, let's let (8,7) be (x₁, y₁) and let's let (2,3) be (x₂, y₂).

Substitute them into our distance formula:

Subtract:

Square:

Add:

Simplify:

So, the distance between the school and the theater is 2√3 units or approximately 7.21 units.

And we're done!

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.